2-ancestry mixing, zero discriminant

Average Accuracy: 74.8% → 98.7%

Time: 9.4s

Precision: binary64

Cost: 13120

Math

\[\sqrt[3]{\frac{g}{2 \cdot a}} \]

↓

\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \]

FPCore

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))

↓

(FPCore (g a) :precision binary64 (* (cbrt g) (cbrt (/ 0.5 a))))

C

double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}

↓

double code(double g, double a) {
	return cbrt(g) * cbrt((0.5 / a));
}

Java

public static double code(double g, double a) {
	return Math.cbrt((g / (2.0 * a)));
}

↓

public static double code(double g, double a) {
	return Math.cbrt(g) * Math.cbrt((0.5 / a));
}

Julia

function code(g, a)
	return cbrt(Float64(g / Float64(2.0 * a)))
end

↓

function code(g, a)
	return Float64(cbrt(g) * cbrt(Float64(0.5 / a)))
end

Wolfram

code[g_, a_] := N[Power[N[(g / N[(2.0 * a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]

↓

code[g_, a_] := N[(N[Power[g, 1/3], $MachinePrecision] * N[Power[N[(0.5 / a), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.8%

   \[\sqrt[3]{\frac{g}{2 \cdot a}} \]

2. Applied egg-rr 98.7%

   \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}}} \]
   Proof

   [Start] 74.8	\[ \sqrt[3]{\frac{g}{2 \cdot a}} \]
   div-inv [=>] 74.8	\[ \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}} \]
   cbrt-prod [=>] 98.7	\[ \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}} \]
   associate-/r* [=>] 98.7	\[ \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\frac{1}{2}}{a}}} \]
   metadata-eval [=>] 98.7	\[ \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{0.5}}{a}} \]

3. Final simplification 98.7%

   \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}} \]

Alternatives

Alternative 1
Accuracy	74.9%
Cost	6720

\[\sqrt[3]{g \cdot \frac{0.5}{a}} \]

Alternative 2
Accuracy	74.8%
Cost	6720

\[\sqrt[3]{\frac{g}{a \cdot 2}} \]

Reproduce

herbie shell --seed 2023137 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))